Non-probability set theory based bounded uncertainty structure static response upper and lower bound assessment method

Abstract

The present invention discloses a non-probability set theory based bounded uncertainty structure static response upper and lower boundary assessment method. The method comprises: firstly, according to the Krein-Milman Theorem, representing any point in an uncertainty parameter interval as a linear combination of a vertex of the uncertainty parameter interval; based on the Clemm Rule, establishing a bounded uncertainty structure static response solving model; and by means of a combined structure vertex stiffness matrix and a vertex load vector, decomposing the model into a series of sub-models and performing a solution separately by combining a parallel algorithm, so as to obtain an upper bound and a lower bound of a bounded uncertainty structure static response, and at the same time, giving a structure parameter corresponding to the upper bound and the lower bound. According to the method disclosed by the present invention, the precise bounds of the bounded uncertainty structure static response can be obtained, and objective and effective data can be provided for reliability assessment and design of structures.

Description

technical field [0001] The invention is mainly applicable to the evaluation of the static response boundary of the bounded uncertainty structure, and specifically relates to an evaluation method of the upper and lower bounds of the static response of the bounded uncertainty structure based on non-probability set theory. Background technique [0002] Traditionally, structural static problems are analyzed and solved based on deterministic models. However, the latest engineering design and research progress have recognized that there are many types of uncertainties in practical engineering. An important problem faced by existing structural analysis and design theories is how to deal with uncertain parameters in structural systems and excitation loads. [0003] Probabilistic methods were first applied to the analysis of structures with uncertain parameters. This method describes the uncertainty information of the system through the probability distribution function (or probabil...

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Problems solved by technology

However, with the increase of the bounded uncertainty parameter, the overestimation of the results of this method is very serious

[0005] At present, for the evaluation of the static response of structures with bounded uncertainties, it has not been possible to obtain an accurate response boundary from theoretical proofs.

In addition, the existing solution models and uncertainty propagation analysis methods often lose their practical application significance due to obtaining too wide interval boundaries, and cannot provide objective and effective data for structural reliability assessment and design

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